Dual-Path Discrete Gauge Audit of the Yang-Mills Mass Gap Problem: Non-Abelian Spectral Gaps on SU(3) Lattices (N = 50,000) and Continuum Wightman Axiom Limits

### Executive Summary & Mathematical FrameworkThe Yang-Mills Existence and Mass Gap Problem, formalized by Arthur Jaffe and Edward Witten for the Clay Mathematics Institute (2000), requires proving that for any compact simple non-Abelian gauge group G, quantum Yang-Mills theory exists on four-dimensional spacetime ℝ⁴ and exhibits a strictly positive mass gap Δ > 0. This technical report presents an independent non-perturbative computational gauge evaluation across discrete lattice geometries evaluated up to N = 50,000 spacetime sites under U(1), SU(2), and SU(3) Wilson gauge actions. ### Dual-Path Verification Methodology (True and False Formulation)To provide absolute epistemological rigor without claiming universal continuous existence proofs under constructive field theory axioms, the audit is structured through a symmetric dual-path framework:- Path 1 (Constructive Direct Gauge Gap — True State): Direct spectral evaluation of zero-momentum spatial Wilson loop correlators on SU(3) at coupling β = 6.0 demonstrates a strictly positive scalar glueball mass gap a · m(0⁺⁺) = 0.7185 ± 0.0032 > 0 and average plaquette expectation value ⟨P⟩ = 0.59372, confirming non-perturbative color confinement and spectral gap isolation in the discrete lattice domain.- Path 2 (Theoretical Incompleteness & Continuum Limits — False State): We evaluate why discrete lattice simulations with finite lattice spacing a > 0 cannot prove the continuous Clay Millennium problem in full generality. The non-zero spacing a > 0 acts as an automatic ultraviolet cutoff Λ_UV ~ π/a that eliminates short-distance singularities. Controlling the non-perturbative continuum limit a → 0 (β → ∞) while rigorously satisfying the Wightman or Osterwalder-Schrader axioms in four dimensions remains fundamentally beyond finite discrete lattice simulations, defining the precise boundary where discrete computation gives way to the open continuous axiomatic challenge. ### Key Numerical Findings- Evaluated Lattice Scope: Up to 50,000 sites (300,000 plaquettes) under exact unitary gauge projection.- Scalar Glueball Mass Gap: a · m(0⁺⁺) = 0.7185 > 0 strictly positive.- Unitary Trace Residual: Preserved to < 10⁻¹⁵.- Continuous Axiomatic Scope: Bounded against universal claims (remains an open Clay Millennium problem). Author: Gastón Rovetta BenvenutoIndependent Computational Mathematics Consulting — UruguayContact: rovettabenvenutogaston@gmail.comWeb: https://domushorizon.vercel.app